Publications with references to Normaliz [1] ABBOTT, J., AND BIGATTI, A. M. What is new in CoCoA? In Mathemat- ical software – ICMS 2014. 4th international congress, Seoul, South Korea, August 5–9, 2014. Proceedings. Berlin: Springer, 2014, pp. 352–358. [2] ABBOTT, J., AND BIGATTI, A. M. New in cocoa-5.2. 2 and cocoalib- 0.99560 for sc-square. In SC2@ ISSAC (2017). [3] AHMED, M., DE LOERA JESUS´ , AND HEMMECKE, R. Polyhedral cones of magic cubes and squares. In Discrete and computational geometry. The Goodman-Pollack Festschrift. Berlin: Springer, 2003, pp. 25–41. [4] AHMED, M. M. Algebraic combinatorics of magic squares. PhD thesis, University of California, Davis, 2004. [5] AL-AYYOUB, I., JARADAT, I., AND AL-ZOUBI, K. On the normality of a class of monomial ideals via the newton polyhedron. Mediterranean Journal of Mathematics 16, 3 (2019), 77. [6] ALCANTAR´ , A. The equations of the cone associated to the rees algebra of the ideal of square-free k-products. Morfismos 5, 1 (2001), 17–27. [7] ALIEV, I., DE LOERA, J. A., AND LOUVEAUX, Q. Integer programs with prescribed number of solutions and a weighted version of Doignon-Bell- Scarf’s theorem. In Integer programming and combinatorial optimization, vol. 8494 of Lecture Notes in Comput. Sci. Springer, Cham, 2014, pp. 37– 51. 1 [8] ALIEV, I., DE LOERA, J. A., AND LOUVEAUX, Q. Semigroups of poly- hedra with prescribed number of lattice points and the k-frobenius problem. arXiv preprint arXiv:1409.5259 (2014). [9] ALIEV, I., DE LOERA, J. A., AND LOUVEAUX, Q. Parametric polyhedra with at least k lattice points: Their semigroup structure and the k-frobenius problem. In Recent trends in Combinatorics. Springer, 2016, pp. 753–778. [10] ALTMANN, K., AND KASTNER, L. Negative deformations of toric sin- gularities that are smooth in codimension two. In Deformations of surface singularities. Berlin: Springer; Budapest: Janos´ Bolyai Mathematical So- ciety, 2013, pp. 13–55. [11] ASSARF, B., GAWRILOW, E., HERR, K., JOSWIG, M., LORENZ, B., PAFFENHOLZ, A., AND REHN, T. Computing convex hulls and counting integer points with polymake. Mathematical Programming Computation 9, 1 (2017), 1–38. [12] ASSI, A., AND GARC´IA-SANCHEZ´ , P. A. Numerical semigroups and applications. Cham: Springer, 2016. [13] AVIS, D., AND JORDAN, C. mplrs: A scalable parallel vertex/facet enu- meration code. Mathematical Programming Computation 10, 2 (2018), 267–302. [14] BACHLE¨ , A., AND CAICEDO, M. On the prime graph question for almost simple groups with an alternating socle. International Journal of Algebra and Computation 27, 03 (2017), 333–347. [15] BACHLE¨ , A., HERMAN, A., KONOVALOV, A., MARGOLIS, L., AND SINGH, G. The status of the zassenhaus conjecture for small groups. Ex- perimental Mathematics (2017), 1–6. [16] BACHLE¨ , A., KIMMERLE, W., AND MARGOLIS, L. Algorithmic aspects of units in group rings. In Algorithmic and Experimental Methods in Alge- bra, Geometry, and Number Theory. Springer, 2017, pp. 1–22. [17] BACHLE¨ , A., AND MARGOLIS, L. On the prime graph question for inte- gral group rings of 4-primary groups I. Internat. J. Algebra Comput. 27, 6 (2017), 731–767. 2 [18] BACHLE¨ , A., AND MARGOLIS, L. Help: a gap package for torsion units in integral group rings. Journal of Software for Algebra and Geometry 8, 1 (2018), 1–9. [19] BECK, M., HAASE, C., AND SAM, S. V. Grid graphs, Gorenstein poly- topes, and domino stackings. Graphs Comb. 25, 4 (2009), 409–426. [20] BECK, M., ROBINS, S., AND SAM, S. V. Positivity theorems for solid- angle polynomials. Beitr. Algebra Geom. 51, 2 (2010), 493–507. [21] BERNSTEIN, D. I., AND SULLIVANT, S. Normal binary hierarchical mod- els. Exp. Math. 26, 2 (2017), 153–164. [22] BIGDELI, M., HERZOG, J., HIBI, T., QURESHI, A. A., AND SHIKAMA, A. Isotonian algebras. Nagoya Math. J. 230 (2018), 83–101. [23] BOFFI, G., AND LOGAR, A. Computing Grobner¨ bases of pure binomial n ideals via submodules of Z . J. Symb. Comput. 47, 10 (2012), 1297–1308. [24] BOFFI, G., AND LOGAR, A. Border bases for lattice ideals. Journal of Symbolic Computation 79 (2017), 43–56. [25] BOGART, T., HAASE, C., HERING, M., LORENZ, B., NILL, B., PAF- FENHOLZ, A., ROTE, G., SANTOS, F., AND SCHENCK, H. Finitely many smooth d-polytopes with n lattice points. Isr. J. Math. 207 (2015), 301–329. [26] BOGART, T., RAYMOND, A., AND THOMAS, R. Small Chvatal´ rank. Math. Program. 124, 1-2 (B) (2010), 45–68. [27] BOHM¨ , J., DECKER, W., KEICHER, S., AND REN, Y. Current challenges in developing open source computer algebra systems. In Mathematical as- pects of computer and information sciences. 6th international conference, MACIS 2015, Berlin, Germany, November 11–13, 2015. Revised selected papers. Cham: Springer, 2016, pp. 3–24. [28] BOHM¨ , J., EISENBUD, D., AND NITSCHE, M. J. Decomposition of semi- group algebras. Exp. Math. 21, 4 (2012), 385–394. [29] BONANZINGA, V., ESCOBAR, C. A., AND VILLARREAL, R. H. On the normality of Rees algebras associated to totally unimodular matrices. Re- sult. Math. 41, 3-4 (2002), 258–264. 3 [30] BOROWKA, S., HEINRICH, G., JAHN, S., JONES, S., KERNER, M., AND SCHLENK, J. Numerical evaluation of two-loop integrals with pysecdec. arXiv preprint arXiv:1712.05755 (2017). [31] BOROWKA, S., HEINRICH, G., JAHN, S., JONES, S., KERNER, M., AND SCHLENK, J. A gpu compatible quasi-monte carlo integrator interfaced to pysecdec. Computer Physics Communications (2019). [32] BOROWKA, S., HEINRICH, G., JAHN, S., JONES, S., KERNER, M., SCHLENK, J., AND ZIRKE, T. pysecdec: a toolbox for the numerical eval- uation of multi-scale integrals. Computer Physics Communications 222 (2018), 313–326. [33] BOROWKA, S., HEINRICH, G., JONES, S., KERNER, M., SCHLENK, J., AND ZIRKE, T. Secdec-3.0: numerical evaluation of multi-scale integrals beyond one loop. Computer Physics Communications 196 (2015), 470– 491. [34] BOUCKAERT, R., HEMMECKE, R., LINDNER, S., AND STUDENY´ , M. Efficient algorithms for conditional independence inference. J. Mach. Learn. Res. 11 (2010), 3453–3479. [35] BRANDT, F., GEIST, C., AND STROBEL, M. Analyzing the practical rel- evance of voting paradoxes via Ehrhart theory, computer simulations, and empirical data. In Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems (2016), International Founda- tion for Autonomous Agents and Multiagent Systems, pp. 385–393. [36] BRENNAN, J. P., DUPONT, L. A., AND VILLARREAL, R. H. Duality, a- invariants and canonical modules of rings arising from linear optimization problems. Bull. Math. Soc. Sci. Math. Roum., Nouv. Ser.´ 51, 4 (2008), 279– 305. [37] BREUER, F. An invitation to Ehrhart theory: polyhedral geometry and its applications in enumerative combinatorics. In Computer algebra and polynomials. Springer International Publishing, 2015, pp. 1–29. [38] BREUER, F., AND ZAFEIRAKOPOULOS, Z. Polyhedral omega: a new algorithm for solving linear Diophantine systems. Ann. Comb. 21, 2 (2017), 211–280. 4 [39] BRUNS, W. On the integral Caratheodory´ property. Exp. Math. 16, 3 (2007), 359–365. [40] BRUNS, W. The quest for counterexamples in toric geometry. In Commuta- tive algebra and algebraic geometry. Proceedings of the international con- ference (CAAG-2010), Bangalore, India, December 6–10, 2010, in honour of Balwant Singh, Uwe Storch and Rajendra V. Gurjar. Mysore: Ramanu- jan Mathematical Society, 2013, pp. 45–61. [41] BRUNS, W. Binomial regular sequences and free sums. Acta Math. Viet- nam. 40, 1 (2015), 71–83. [42] BRUNS, W., AND CONCA, A. Linear resolutions of powers and products. In Singularities and Computer Algebra. Springer, 2017, pp. 47–69. [43] BRUNS, W., AND CONCA, A. Products of Borel fixed ideals of maximal minors. Adv. Appl. Math. 91 (2017), 1–23. [44] BRUNS, W., GARCIA-SANCHEZ, P., O’NEILL, C., AND WILBURNE, D. Wilf’s conjecture in fixed multiplicity. arXiv preprint arXiv:1903.04342 (2019). [45] BRUNS, W., GARC´IA-SANCHEZ´ , P. A., AND MOCI, L. The monoid of monotone functions on a poset and arithmetic multiplicities for uniform matroids. arXiv preprint arXiv:1902.00864 (2019). [46] BRUNS, W., AND GUBELADZE, J. Normality and covering properties of affine semigroups. J. Reine Angew. Math. 510 (1999), 161–178. [47] BRUNS, W., AND GUBELADZE, J. Polytopes, rings, and K-theory. New York, NY: Springer, 2009. [48] BRUNS, W., GUBELADZE, J., HENK, M., MARTIN, A., AND WEISMAN- TEL, R. A counterexample to an integer analogue of Caratheodory’s´ theo- rem. J. Reine Angew. Math. 510 (1999), 179–185. [49] BRUNS, W., GUBELADZE, J., AND MICHAŁEK, M. Quantum jumps of normal polytopes. Discrete Comput. Geom. 56, 1 (2016), 181–215. [50] BRUNS, W., GUBELADZE, J., AND NGOˆ VIETˆ TRUNG. Problems and algorithms for affine semigroups. Semigroup Forum 64, 2 (2002), 180– 212. 5 [51] BRUNS, W., ICHIM, B., AND SOGER¨ , C. Computations of volumes and Ehrhart series in four candidates elections. Annals of Operations Research (2019), 1–25. [52] BRUNS, W., AND RESTUCCIA, G. Canonical modules of Rees algebras. J. Pure Appl. Algebra 201, 1-3 (2005), 189–203. [53] BUBBOLONI, D., DISS, M., AND GORI, M. Extensions of the simp- son voting rule to the committee selection setting. https://halshs.archives- ouvertes.fr/halshs-01827668/ (2017). [54] BURTON, B. A. Computational topology with Regina: algorithms, heuris- tics and implementations. In Geometry and topology down under. A con- ference in honour of Hyam Rubinstein, Melbourne, Australia, July 11– 22, 2011. Proceedings. Providence, RI: American Mathematical Society (AMS), 2013, pp. 195–224. [55] BURTON, B. A., AND OZLEN, M. Computing the crosscap number of a knot using integer programming and normal surfaces. ACM Trans. Math. Softw. 39, 1 (2012), 18. [56] CABOARA, M., AND FARIDI, S. Odd-cycle-free facet complexes and the Konig¨ property. Rocky Mt. J. Math. 41, 4 (2011), 1059–1079. [57] CAMERON, A., DINU, R., MICHAŁEK, M., AND SEYNNAEVE, T. Flag matroids: algebra and geometry. arXiv preprint arXiv:1811.00272 (2018).